1. Field of the Invention
The present invention relates to a digital-to-analog converter for converting discrete digital data into continuous analog signals. In this specification, it is assumed that a case where function values have finite values except zero in a local region and become zero in regions different from the region is called a xe2x80x9clocal support.xe2x80x9d
2. Description of the Prior Art
A recent digital audio apparatus, for example, a CD (Compact Disk) player, uses a D/A (digital-to-analog) converter to which an over-sampling technique is applied to obtain a continuous analog audio signal from discrete music data (digital data). Such a D/A converter generally uses a digital filter to raise a pseudo sampling frequency by interpolating input digital data, and outputs smooth analog voice signals by passing each interpolation value through a low-pass filter after generating a staircase signal waveform with each interpolation value held by the sample holding circuit.
A data interpolating process is performed with a digital filter contained in a D/A converter using a sampling function generally referred to as a sinc function. FIG. 16 is an explanatory graph of a sinc function. This sinc function is obtained when a Dirac delta function is inverse-Fourier-transformed, and is defined as sin (xcfx80ft)/(xcfx80ft) where the sampling frequency is f. This sinc function becomes one only at a sample point, where t=0, and zero at all other sample points.
Conventionally, an oversampling process is performed using a digital filter in which a waveform data of the sinc function is set to a tap counter of an FIR (finite impulse response) filter.
In the oversampling technology for performing an interpolating operation on discrete voice data using a digital filter, a low-pass filter having a moderate attenuation characteristic can be applied. Therefore, the phase characteristic with a low-pass filter can approach a linear phase characteristic, and the sampling aliasing noise can be reduced. Such an effect becomes more outstanding with a higher pseudo sampling frequency. However, when a sampling frequency rises, the processing speed of the digital filter and the sample holding circuit is also increased. Therefore, expensive parts applied in the high-speed process are required, thereby raising the entire parts cost. In addition, when a high sampling frequency (for example, several MHz) is necessary for image data, etc., a digital filter for oversampling and a sample holding circuit have to be mounted using parts operated around several ten MHz to several hundred MHz, which cannot be easily realized.
In addition, even when the oversampling technology is used, a smooth analog signal is generated by passing a staircase signal waveform through a low-pass filter. Therefore, when a low-pass filter is used, a linear phase characteristic in the strict sense cannot be expected. Furthermore, the above mentioned sinc function is a function converging to 0 at xc2x1∞. Therefore, when a correct interpolation value is computed, all digital data values should be considered. However, for convenience of a circuit size, etc., the number of tap counters of a digital filter is set so as to the range of digital data to be taken into account is limited. Therefore, an obtained interpolation value contains a truncation error.
Thus, the conventional D/A converter using the oversampling technology requires parts for a high-speed operation to raise a pseudo sampling frequency, thereby incurring a high cost or realizing a necessary system with difficulty. Furthermore, the deterioration of the phase characteristic arises from using a low-pass filter, and a truncation error is contained because the digital filter to which a sinc function is applied is used. Therefore, distortion of output waveform according to the deterioration of the phase characteristic and the truncation error occurs.
The present invention has been developed based on the above mentioned problems, the object of the present invention is to provide a digital-to-analog converter capable of obtaining an output waveform with less distortion without increasing the speed of operating parts.
A digital-to-analog converter of the invention comprises generating the step function waveforms having the voltage levels corresponding to respective input digital data, synthesizing the generated step function waveforms, and making the analog integral operations plural times to produce a continuous analog signal that connects smoothly the voltages corresponding to the digital data input successively. In this way, because of generating the predetermined step function waveforms corresponding to plural digital data input successively, synthesizing the generated step function waveforms, then integrating synthesized waveforms to get a continuous analog signal, there is no need of using a low-pass filter to get a final analog signal. Therefore, there is no deterioration of the group delay characteristic caused by variable phase characteristic depending on the frequency of a signal to be processed, resulting in an output waveform with less distortion. Also, since there is no need of speeding up the operation rate of parts, and using expensive parts, unlike the conventional method that performed the oversampling, it is possible to reduce the part costs.
In particular, the above-described step function waveform is preferably obtained by differentiating a sampling function consisting of a piecewise polynomial multiple times. On the contrary, the waveform corresponding to the predetermined sampling function can be obtained by integrating this step function waveform multiple times. Therefore, the convolution operation using the sampling function can be equivalently performed generating the step function waveform, so that the processing contents can be simplified, and the volume of processing required for converting digital data to analog signal can be reduced.
The above-described sampling function is preferably differentiable only once over the whole range, and has values of a local support. It is considered that it is necessary that various signals existing in the natural world have differentiability because the signals change smoothly. Nevertheless, it is considered that it is not necessary that the differentiability is not always infinite, and that it is possible to sufficiently approximate natural phenomena so long as the signal scan be differentiated only once. In this manner, although there are many advantages by using a sampling function of the local support that can be differentiated finite times, conventionally, it was considered that a sampling function fulfilling these conditions did not exist. Nevertheless, by the present inventor""s research, a function fulfilling the conditions described above is found.
More specifically, the above-described sampling function is a function of local support having the values other than zero in a range where the sample point t is from xe2x88x922 to +2. This sampling function is defined such that:
(xe2x88x92t2xe2x88x924txe2x88x924)/4 for xe2x88x922xe2x89xa6t less than xe2x88x923/2,
(3t2+8t+5)/4 for xe2x88x923/2xe2x89xa6t less than xe2x88x921,
xe2x80x83(5t2+12t+7)/4 for xe2x88x921xe2x89xa6t less than xe2x88x921/2,
(xe2x88x927t2+4)/4 for xe2x88x921/2xe2x89xa6t less than 1/2,
(5t2xe2x88x9212t+7)/4 for 1/2xe2x89xa6t less than 1,
(3t2xe2x88x928t+5)/4 for 1xe2x89xa6t less than 3/2,
and
(xe2x88x92t2+4txe2x88x924)/4 for 3/2xe2x89xa6txe2x89xa62
Or a step function waveform corresponding to such a sampling function may consist of eight piece wise sections in equal width with a weight of xe2x88x921, +3, +5, xe2x88x927, xe2x88x927, +5, +3, and xe2x88x921 in a predetermined range corresponding to five digital data arranged at an equal interval.
In this way, the use of a sampling function differentiable only once over the whole range, the number of integrating operation after synthesizing a plurality of a step function waveforms can be decreased, and the amount of calculation can be reduced. Also, because of the use of a sampling function having values of a local support, it is possible to handle only digital data corresponding to a section for the local support, so that the amount of calculation can be further reduced. Moreover, it is possible to prevent the truncation error from arising when the process is performed for the finite number of digital data.